Sasha is lucky to have a diamond in the form of a regular tetrahedron. Incidentally, his friend Pasha has got a diamond of exactly the same shape and size. In order to distinguish between their diamonds, the friends decided to paint the crystals. Each of them painted each face of his diamond a certain color. The diamonds became very beautiful, so Pasha and Sasha were happy. But their happiness did not last long. That night, Sasha woke up with a sudden thought — what if his and Pasha's diamonds are still indistinguishable? He decided to call Pahsa immediately. Sasha ran up to the phone, tried to grasp the receiver, but at that moment the phone rang. Of course, it was Pasha, who had the same sudden thought. So Sasha and Pasha hastened to tell each other the colors of their diamonds' faces… Their worst fears were confirmed. Their diamonds were identical, and to see it one simply had to turn one of the diamonds.
You are to write a program that could prevent this horrible
mistake. Given a scheme of the supposed coloring of the diamonds,
determine if these colorings are identical, i.e., if one of them
can be obtained from the other by turning the crystal.
The input contains two lines. Each line contains four letters, which denote the colors of the faces in the following order: the base face, the "left front" face, the "right front" face, and the back face. There are only four paints available: red, green, blue, and yellow, denoted by the letters R, G, B, and Y, respectively.
Output the word "equal" if the colored tetrahedrons will be
identical, and the word "different" otherwise.
Problem Author: Pavel Egorov, Stanislav Vasilyev
Problem Source: The 7th USU Open Personal Contest - February 25, 2006